Abstract
In this paper, we introduce a modified Mann iterative process for strictly pseudocontractive mappings and obtain a strong convergence theorem in the framework of Hilbert spaces. Our results improve and extend the recent onesannounced by many others.
Highlights
(If (1.1) holds, we say that T is a k -strict pseudocontraction.) Strict pseudocontractions in Hilbert spaces were introduced by Browder and Petryshyn (1967, 197-228), which are extension of extensions of nonexpansive mappings which satisfy the inequality (1.1) with k = 0
Mann's iteration process has no strong convergence for nonexpansive maps even in Hilbert spaces (Genel & Lindenstrass, 1975, 81-86)
Studied the viscosity approximation methods proposed by Moudafi (2000, 46-55) for nonexpansive mappings in a uniformly smooth Banach space
Summary
N n=0 is in the interval is often used to approximate a fixed point of a nonexpansive mapping. Mann's iteration process has no strong convergence for nonexpansive maps even in Hilbert spaces (Genel & Lindenstrass, 1975, 81-86). (2005, 51-60) modified Mann iterative process to get a strong convergence theorem for nonexpansive mappings.
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